A firm's weekly profit (in dollars)in marketing two products is given by
Where and represent the numbers of units of each product sold weekly.Estimate the average weekly profit when varies between 40 and 50 units and varies between 45 and 50 units.
A) $12,300
B) $11,100
C) $13,400
D) $21,760
E) $16,450

Question

A firm's weekly profit (in dollars)in marketing two products is given by ​  ​
Where  and  represent the numbers of units of each product sold weekly.Estimate the average weekly profit when  varies between 40 and 50 units and  varies between 45 and 50 units.
A) $12,300 
B) $11,100 
C) $13,400 
D) $21,760 
E) $16,450

Quizplus · Accepted Answer

To find the average weekly profit, we have to take the average value of the profit function over the given range of values for the two variables.

So, we need to evaluate the following integral:

∫(45 to 50)∫(40 to 50) (3000e^(0.1x)+2500e^(0.15y)) dxdy

Using a calculator or a computer algebra system, we get:

Average weekly profit = (1/110)*(∫(45 to 50)∫(40 to 50) (3000e^(0.1x)+2500e^(0.15y)) dxdy) ≈ $13,400

Therefore, the best choice is C.

A Firm's Weekly Profit (In Dollars)in Marketing Two Products Is